Electrochemical impedance measurement systems generally use the Bode analysis as a well-established and proven technique to characterize an impedance of an energy storage device (ESD). The ESD under evaluation is excited with an input signal at a given frequency, and the response is measured. This process is sequentially repeated over a range of frequencies until the impedance spectrum is obtained. This method is effective in assessing ESD degradation over time and usage, but it requires expensive laboratory equipment, and it can be time consuming given the serial measurement approach.
An alternative approach using bandwidth limited noise as an excitation signal can also be used to obtain the impedance more quickly. The electrochemical impedance measurement system response to noise is processed with correlations and Fast Fourier Transform (FFT) algorithms. This technique was developed at the Idaho National Laboratory (U.S. Pat. No. 7,675,293) and successfully applied to various battery technologies (Christophersen et al., 2008). However, this approach requires the average of multiple measurements to adequately determine the impedance response over the desired frequency range, which also makes it more of a serial approach.
Rapid, in-situ acquisition of ESD impedance data over a desired frequency range can be implemented with Compensated Synchronous Detection (CSD) and Fast Summation Transformation (FST). Unlike typical AC impedance measurements and noise analysis methods, these techniques are parallel approaches that require only a single time record to capture the ESD response. As a result, both CSD and FST are well-suited for onboard applications that require impedance measurements as part of an overall smart monitoring system used for control and diagnostics.
Compensated Synchronous Detection (U.S. Pat. No. 7,395,163) is a technique that inputs an excitation signal consisting of a select number of logarithmically distributed frequencies in a sum-of-sines (SOS) configuration. The duration of the SOS excitation signal depends on the frequency step factor and the desired resolution of the impedance spectrum. Typical CSD measurements require a minimum of three periods of the lowest frequency (Morrison et al., “Real Time Estimation of Battery Impedance,” Proceedings from the IEEE Aerospace Conference, 2006). A time record of the ESD response to the SOS excitation signal is also captured at an appropriate sample rate. The resulting data are used to calculate impedance using synchronous detection to estimate the “In Phase” and the “Quadrature” components at each frequency. Because of cross-talk error, a Compensation Time Record (CTR) is created by reassembling all of the detected responses except for the frequency of interest. This suppresses all of the other frequency components and allows the frequency of interest to be detected with greatly reduced corruption from cross-talk (Morrison et al., “Real Time Estimation of Battery Impedance,” Proceedings from the IEEE Aerospace Conference, 2006). The CTR is then subtracted from the originally captured response signal, and the result is synchronously detected again. This process is repeated at each frequency of interest to achieve an impedance spectrum with minimal error. The “In Phase” and “Quadrature” components can be easily converted to magnitude and phase angle with simple trigonometric relations.
Fast Summation Transformation (Morrison et al., “Fast Summation Transformation for Battery Impedance Identification,” Proceedings from the IEEE Aerospace Conference, 2009) is a variation of CSD. It is based on an SOS input signal using octave harmonics to cover the desired frequency range (U.S. Pat. No. 8,150,643). Since cross-talk error is eliminated with octave harmonics, only one period of the lowest frequency is required to complete the measurement and obtain the impedance spectrum. A time record of the ESD response to the SOS excitation signal is also captured at an appropriate sample rate. The FST detection process obtains the “In Phase” and “Quadrature” components by first rectifying the response signal relative to the sine and cosine at each frequency of interest, adding up all the data points in the rectified signal, normalizing to the number of periods of the given frequency, and then storing that result. Results from these rectified responses are placed in a two-element vector (sine and cosine), and multiplied by a conversion matrix (U.S. Pat. No. 8,150,643) to yield the “In Phase” and the “Quadrature” components at the desired frequency. This process is repeated for each of the octave frequencies in the SOS. The “In Phase” and “Quadrature” components can be easily converted to magnitude and phase angle with simple trigonometric relations.